In passband communication systems, a transmitted signal typically undergoes time offset (delay), phase shift, and attenuation (amplitude change). These effects must be compensated for at the receiver.
Estimation of time offset is critical for good receiver performance. The ability to improve the estimation accuracy for this time offset can be translated into a number of valuable benefits, including increased receiver sensitivity, increased power efficiency, a reduction in the amount of overhead required for pilot/training sequences.
A transmitted signal contains pilot symbols and data symbols. Signalling constellations that have symbols on the complex unit circle such as binary phase shift keying (BPSK), quaternary phase shift keying (QPSK) and M-ary phase shift keying (M-PSK) are often used, but more generally, quadrature amplitude modulated (QAM) constellations can also be used.
The problem of estimating time offset has undergone considerable prior research. Traditional approaches involve analogue phase-lock-loops and digital implementations motivated by phase-lock-loops. These approaches focus on estimating τ0 modulo the symbol period T, that is, if τ0=γ0+i0T where i0εZ and γ0ε[−T/2, T/2), then an estimator of γ0 is given. This estimate may be used to drive a sampling device applied to the received signal (usually after matched filtering). Some other method must then be used to align the samples, i.e., to estimate i0. The problem of estimating γ0 is usually called symbol synchronisation, while the second problem of estimating i0 is usually called frame synchronisation.
More recently iterative methods attempting to exploit the error correcting code used by the transmitter have appeared. These estimators typically apply the expectation maximisation (EM) algorithm under a Gaussian assumption regarding the noise w(t). A key problem is that the EM algorithm converges correctly only if initialised at some τ sufficiently close to τ0. Methods for efficiently obtaining a τ close to τ0 are still required.